Hazel and Vanessa collected buttons. Hazel gave 30% of her buttons to Vanessa and as a result, Vanessa's buttons increased by 10%. If Hazel had 77 buttons left, find the number of buttons Vanessa should give to Hazel in the end so that both had an equal number of buttons.

	Hazel	Vanessa	Comparing the change in Vanessa's buttons
Before	10x1 = 10 u		10x3 = 30u
Change	- 3x1 = - 3 u	+ 3x1 = + 3 u	+ 1x3 = + 3 u
After	7x1 = 7 u		11x3 = 33 u

30% = ³⁰₁₀₀ = ³₁₀
10% = ¹⁰₁₀₀ = ¹₁₀

The increase in the number of buttons that Vanessa had is repeated.  Make the increase in the number of buttons that Vanessa had the same. LCM of 3 and 1 = 3

7 u = 77

1 u = 77 ÷ 7 = 11

Number of buttons that Vanessa had more than Hazel in the end
= 33 u - 7 u
= 26 u

Number of buttons that Vanessa should give to Hazel so that both had an equal number of buttons in the end
= 26 u ÷ 2
= 13 u
= 13 x 11
= 143

Answer(s): 143